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Perfect Domination in Knights Graphs

2018/05/09 by Todd Fenstermacher, Fenstermacher, Todd, Soumendra Ganguly +3
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1805.03335

openalex publication_date 2018/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a graph G = (V,E), a subset S of V is a perfect dominating set of G if every vertex not in S is adjacent to exactly one vertex in S. The perfect domination number, γp(G), is the minimum cardinality of a perfect dominating set of G. The perfect domination number is found for knights graphs on square, rectangular, and infinite chessboards. Indeed, exact values or bounds are given for all chessboards except those with 3 rows and number of columns congruent to 1, 2, or 3 modulo 8.

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